Cantor Set and its properties

Authors

  • Bryan Douglas Nunes Assunção Universidade Federal de Uberlândia (UFU), Instituto de Física, Graduação em Física de Materiais, Uberlândia, MG, Brasil https://orcid.org/0000-0002-4715-3392
  • Fábio José Bertoloto Universidade Federal de Uberlândia (UFU), Faculdade de Matemática, Uberlândia, MG, Brasil https://orcid.org/0000-0002-2212-2602

DOI:

https://doi.org/10.35819/remat2021v7i1id4394

Keywords:

Cantor Set, Countable Sets, Homeomorphic Sets, Topolical Notions on the Real Line

Abstract

This work intends to publicize the already well-known Cantor set. The idea is to show a more detailed demonstration of some important properties that it has, in a certain way being not very common to find in texts in Portuguese. We will also see that, except for homeomorphism, the Cantor Set is the only one, as metric space, with all the indicated properties.

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Author Biographies

Bryan Douglas Nunes Assunção, Universidade Federal de Uberlândia (UFU), Instituto de Física, Graduação em Física de Materiais, Uberlândia, MG, Brasil

http://lattes.cnpq.br/7534710091311367

Fábio José Bertoloto, Universidade Federal de Uberlândia (UFU), Faculdade de Matemática, Uberlândia, MG, Brasil

http://lattes.cnpq.br/6413209139727471

References

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FREIRA, A. A. A teoria dos conjuntos de cantor. Paidéia, Ribeirão Preto, n. 2, fev./jul. 1992. DOI: https://doi.org/10.1590/S0103-863X1992000200008.

IMPA. Instituto de Matemática Pura e Aplicada. Georg Cantor (1845-1918) - pai do infinito e do ICM. 15 dez. 2017. Disponível em: https://impa.br/noticias/georg-cantor-1845-1918-pai-do-infinito-e-do-icm/. Acesso em: 06 jun. 2020.

LIMA, E. L. Análise Real. v. 1, 12. ed. Rio de Janeiro:

IMPA, 2018.

LIMA, E. L. Curso de Análise. v. 2, 11. ed. Rio de Janeiro: IMPA, 2014.

MATHONLINE. Compact Sets in a Metric Space are Closed and Bounded. Disponível em: http://mathonline.wikidot.com/compact-sets-in-a-metric-space-are-closed-and-bounded. Acesso em: 23 jun. 2020.

MUNKRES, J. R. Topology. 2. ed. New Jersey: Prentice Hall, 2000.

WILLARD, S. General Topology. Mineola N. Y.: Dover Publications, 2004.

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Published

2021-04-20

How to Cite

ASSUNÇÃO, B. D. N.; BERTOLOTO, F. J. Cantor Set and its properties. REMAT: Revista Eletrônica da Matemática, Bento Gonçalves, RS, v. 7, n. 1, p. e3011, 2021. DOI: 10.35819/remat2021v7i1id4394. Disponível em: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4394. Acesso em: 22 jul. 2024.

Issue

Vol. 7 No. 1 (2021)

Section

Mathematics

License

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